GB/T 24637.4-2020Geometrical product specifications (GPS) - General concepts - Part 4: Geometrical characteristics for quantifying GPS deviations (English PDF)

4.1 Overview

Several types of geometric features, as defined in GB/T 38761, are as follows.

--- Essential characteristics. size, shape or surface structure characteristics;

---Azimuth characteristics. position, direction and beating characteristics.

For a geometric feature, the fitting element of the input element is its reference element (see Figure 2).

Note 1.The reference element is the fitting element. For more information, please refer to GB/T 17851.

Note 2.It is assumed that the points in the required range on the reference element meet the correspondence with the corresponding point in the input element. In some cases, mathematical extensions of reference elements are required,

The rules for this extension are not given in this document. For details, please refer to the relevant standards of GPS features.

a) Unconstrained (shape deviation) b) Directional constraint (directional deviation)

c) There are position constraints (local position deviation)

The reference elements for evaluating essential characteristics (size, shape, or surface structure characteristics) are independent of the benchmark system.

The reference element for evaluating the azimuth characteristics is related to the benchmark system (defining direction or location constraints).

Reference elements can be.

---Fully constrained, that is, all non-redundant degrees of freedom are constrained;

--- Partially constrained, that is, not all non-redundant degrees of freedom are constrained.

For geometric features such as shape, direction, position or runout, the shape of the reference element defaults to the nominal shape of the measured element. When tested

The nominal shape of the element belongs to the prism or complex constant class, so its definition is related to the nominal length. In order to define arbitrary bias based on reference elements

Poor, it is necessary to give an unconstrained definition of reference elements. Compared with the nominal shape, the extension of the reference element is defined as the curvature of the nominal shape by default.

continue.

4.2 Types of geometric features

Local geometric deviation is the basic element to establish geometric features.

The direction away from the material is usually regarded as the positive direction.

The default is defined as the minimum distance from a point on the measured element to the reference element (see Figure 3).

Note. The local geometric deviation is defined by any point in the input elements, but for reference elements, this is not necessary. Set of minimum distance and normal distance

The collections need not be the same.

The input feature can be an extracted feature, a filtered feature, or a constrained fitting feature.

If the input feature is a complete line, then the geometric feature is a line geometric feature. If the input feature is a complete surface, then

This geometric feature is a face geometric feature.

If the input element is.

---A derived surface, then the reference space is the surface reference space;

---A line on a complete surface, then the reference space is a line reference space;

---An export line in the space, then the reference space is a two-way reference space;

---An export point, then the reference space is the line reference space;

---A component point, then the reference space is a line or area reference space.

Example. When the input feature is a cylindrical lead-out line (center line), the surface reference space is a cylindrical space.

Any geometric feature is established by the quantization function of the local geometric deviation set (see the example in Table 1).

Each quantization function is built on.

a) Variation curve of local geometric deviation;

b) Change curve of support rate;

c) Amplitude distribution variation curve.

A local coordinate system is defined in the reference space An, and the variation curve of the local geometric deviation is in the reference space (line or surface)

The local geometric deviation set (local coordinate value) in. The curve can be drawn in a reference space that directly displays local coordinate values

(See Figure 5).

Note 1.Since the local geometric deviation is defined by any point of the input feature, there are three possibilities for any coordinate in the reference space. no additional local geometry

Deviation, there is an additional local geometric deviation, and there are multiple additional local geometric deviations (when the input feature is more locally smooth than the reference feature).

The support rate curve is the conversion of the local geometric deviation variation curve. The definition of support ratio is any number between the minimum and maximum

The percentage of entities of any feature.

Note 2.The support rate curve can be understood as the cumulative probability function in the reference space.

The amplitude distribution variation curve is a kind of deformation of the local geometric deviation variation curve. The amplitude distribution variation curve is one of the support ratio curves

A derived definition, which represents the probability in a reference space where the local deviation level is a fixed value.

The geometric features are defined by a quantization function, which is a kind of mathematical operator. The quantization functions given in Table 1 are used in the game

Part of the geometric deviation change curve (see GB/T 38761).

When the geometric characteristics are obtained from the support ratio or the amplitude distribution variation curve, other mathematical operators can also be defined.

Note 3.At any position near the extracted (composed or derived) element, mathematical operators can be used for a certain part of the geometric element. Mathematical operators can be used first

It is used in one direction of the reference space, and then used in other directions, or directly used in the two directions of the reference space. This process can be repeated

Until the geometric feature becomes a global feature.

a For details, see GB/T 3358.1.

bn extraction points, each with a weight wi. When the extracted points of the measured feature are uniformly distributed, the weight of these extracted points is 1.

c When establishing the reference element using the minimum and maximum criterion (Chebyshev criterion without entity constraints), use the "double maximum deviation" formula and

The "range" formula gives the same result.

d For geometric specifications, the target value tau is considered equal to zero.

In the geometric specification, the quantization functions in Table 1 are used to define geometric features.

Figure 6 shows the set of local geometric deviations, which are defined by the signed distance value between the extracted combined element and the reference element. Shown

The local geometric deviation set is a circle with a certain size in the reference system, and these local distances constitute a variation curve.

Appendix A

(Informative appendix)

Relationship with GPS matrix model

A.1 Overview

For the complete details of the GPS matrix model, see GB/T 20308.

The GPS matrix model in GB/T 20308 summarizes the GPS system, and this part is a part of the system. Unless otherwise stated

Obviously, the GPS basic rules given in GB/T 4249 are applicable to this part, and the default rules given in GB/T 18779.1 are applicable in accordance with this part.

Developed specifications.

A.2 Information about standards and their use

This section gives general rules for establishing GPS features.

A.3 Position in GPS matrix model

This part is a general GPS standard. The rules and principles given in this section apply to all marked solid points in the GPS matrix

part.

A.4 Related standards

The standards involved in the standard chain shown in Table A.1 are related standards.

references

[1] GB/T 3358.1 Statistics vocabulary and symbols Part 1.General statistical terms and terms used in probability

[2] GB/T 4249 Geometric Technical Specification for Products (GPS) Basic Principles Concepts, Principles and Rules

[3] GB/T 17851 Product Geometric Technical Specification (GPS) Geometric Tolerance Datum and Datum System

[4] GB/T 18779.1 Product Geometrical Quantity Technical Specification (GPS) Measurement and Inspection of Workpiece and Measuring Equipment Part 1 Press

Standardizing inspection rules for qualified or unqualified

[5] GB/T 20308 Product Geometric Technical Specification (GPS) Matrix Model

[6] GB/T 24637.1 Product Geometric Technical Specification (GPS) General Concept Part 1.Geometric Specification and Inspection Model

[7] GB/T 24637.2 Product Geometric Technical Specification (GPS) General Concept Part 2.Basic Principles, Specifications, Operational Sets and

uncertainty

[8] GB/T 24637.3 Product Geometric Technical Specification (GPS) General Concept Part 3.Measured Elements